Finite Group Databasebeta

← Dic5×#930 #14321480

Subgroups — Dic5×#930 #14321480

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#930C211yesmaximal, characteristic
2C22×C3×C4×Dic5C211yesmaximal, characteristic, complemented
3C2×Dic5×#67C212yesmaximal, complemented
4C2×Dic5×D12C211yesmaximal, characteristic, complemented
5#11751313C211yesmaximal, characteristic, complemented
6#11749492C212yesmaximal, complemented
7Dic5×(C2×D3)⋊C4C212yesmaximal, complemented
8#11748842C211yesmaximal, characteristic, complemented
9#11748764C211yesmaximal, characteristic, complemented
10#11748747C212yesmaximal, complemented
11Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
12Dic5×#121—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C5×#67C2212yes—
15C22×C5×D12C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C23×C3×Dic5C2211yescharacteristic
18C22×D3×Dic5C2212yes—
19C2×#6719C2212yes—
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C5×#930C418yescomplemented
23C2×C5×(C2×D3)⋊C4C2212yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic5—24no—
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30Dic5×#67—28no—
31C2×Dic3⋊Dic5C2212yes—
32C2×(C2×D3)⋊Dic5C2212yes—
33C2×(C2×D3)⋊Dic5C2212yes—
34C2×(C2×D3)⋊Dic5C2212yes—
35C2×Dic3×Dic5C2212yes—
36Dic5×D12—24no—
37#91115C2212yes—
38#90994C2212yes—
39#90994C2212yes—
40C4×#930—51nomaximal, Hall
41C2×C5×#121—31no—
42C2×D4×Dic5—31no—
43C2×D4×Dic5—32no—
44C22×C4×Dic5D311yescharacteristic, complemented
45#65510—31no—
46#65509—32no—
47#65501—31no—
48#65274—31no—
49C4⋊C4×Dic5—31no—
50#65240—32no—
51C22⋊C4×Dic5—32no—
52C24×C3×C5C2311yescharacteristic
53C23×C5×D3C2312yes—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5C2×C414yescomplemented
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15C2312yes—
60C22×Dic15C2312yes—
61C2×C5×#67—24no—
62C2×C5×#67—24no—
63C2×C5×#67C2×C418yescomplemented
64C22×C5×Dic3C2312yes—
65C2×C5×D12—22no—
66C2×C5×D12—22no—
67C2×C5×D12C2×C414yescomplemented
68C22×C3×Dic5—22no—
69C22×C3×Dic5—22no—
70C22×C3×Dic5—22no—
71C22×C3×Dic5—22no—
72C22×C3×Dic5—22no—
73C22×C3×Dic5D414yescomplemented
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C2×D3×Dic5—24no—
79C2×D3×Dic5—24no—
80C2×D3×Dic5—24no—
81#6719—24no—
82C4⋊Dic15—22no—
83C4⋊Dic15—22no—
84C5×(C2×D3)⋊C4C2×C418yescomplemented
85C5×C4⋊Dic3C2×C414yescomplemented
86C3×C4×Dic5—22no—
87C3×C4×Dic5—22no—
88C3×C4×Dic5—22no—
89C3×C4×Dic5D414yescomplemented
90Dic3⋊Dic5—24no—
91(C2×D3)⋊Dic5—24no—
92(C2×D3)⋊Dic5—24no—
93(C2×D3)⋊Dic5—24no—
94Dic3×Dic5—24no—
95C22×C3×C42—51no—
96C2×#930D511yescharacteristic
97C2×C4×#67—52no—
98C2×C4×D12—51no—
99#5213—52no—
100#5212—51no—
101#4940—52no—
102#4939—51no—
103C4×(C2×D3)⋊C4—52no—
104C4×C4⋊Dic3—51no—
105#4928—51no—
106C22×C5×D4—32no—
107C22×C5×D4—31no—
108C23×C4×C5C2×D311yescharacteristic
109C23×Dic5—32no—
110C23×Dic5C2×D311yescharacteristic
111C23×Dic5C2×D311yescharacteristic
112C5×#121—38no—
113C2×C5×C4⋊C4—31no—
114C2×C5×C22⋊C4—32no—
115C2×C22⋊Dic5—32no—
116C2×C22⋊Dic5—32no—
117C2×C22⋊Dic5—32no—
118C2×C22⋊Dic5—32no—
119D4×Dic5—68no—
120D4×Dic5—64no—
121C2×C4⋊Dic5—31no—
122C2×C4⋊Dic5—31no—
123C2×C4⋊Dic5—32no—
124C2×C4×Dic5—24no—
125C2×C4×Dic5—32no—
126C2×C4×Dic5C2×D311yescharacteristic
127C2×C4×Dic5C2×D311yescharacteristic
128C2×C4×Dic5C2×D311yescharacteristic
129C2×C4×Dic5C2×D311yescharacteristic
130#3963—32no—
131#3963—32no—
132#3963—32no—
133C4×#121—151noSylow
134C23×C3×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5—21no—
137C23×C3×C5—21no—
138C23×C3×C5C22×C412yes—
139C23×C3×C5C2×D412yes—
140C23×C3×C5#4112yes—
141C23×C3×C5C2411yescharacteristic
142C22×C5×D3—22no—
143C22×C5×D3—22no—
144C22×C5×D3—22no—
145C22×C5×D3—22no—
146C22×C5×D3—22no—
147C22×C5×D3—22no—
148C22×C5×D3C22×C414yes—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—28no—
152C2×C3×C4×C5C22×C412yes—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5#4112yes—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15—22no—
162C5×#67—216no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3C22×C414yes—
166C5×D12—28no—
167C2×C3×Dic5—28no—
168C2×C3×Dic5—21no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—21no—
173C2×C3×Dic5—21no—
174C2×C3×Dic5—28no—
175C2×C3×Dic5C2×D412yes—
176C2×C3×Dic5C2×D412yes—
177C2×C3×Dic5C2×D412yes—
178C2×C3×Dic5C2×D412yes—
179C2×C3×Dic5#4112yes—
180C2×C3×Dic5#4112yes—
181D3×Dic5—48no—
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×C3×C4C2×D511yescharacteristic
185C22×#67C2×D512yes—
186C22×D12C2×D511yescharacteristic
187C22×C4×D3—52no—
188C2×C3×C42—51no—
189C2×C3×C42—51no—
190C2×C3×C42—51no—
191C2×C3×C42—51no—
192C2×C3×C42—104no—
193C2×#217—52no—
194#930Dic518yesdirect product factor
195C4×#67—108no—
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4C2×D512yes—
200C2×C4⋊Dic3—51no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3C2×D511yescharacteristic
203C2×Dic3⋊C4—52no—
204C2×C4×Dic3—52no—
205C4×D12—104no—
206C3⋊#95—52no—
207C3⋊#95—52no—
208C3⋊#95—52no—
209C24×C5—32no—
210C24×C5C22×D311yescharacteristic
211C2×C5×D4—38no—
212C2×C5×D4—34no—
213C2×C5×D4—64no—
214C2×C5×D4—64no—
215C2×C5×D4—62no—
216C2×C5×D4—62no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—32no—
220C22×C4×C5C4×D314yescomplemented
221C22×C4×C5C22×D311yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—32no—
229C22×Dic5—32no—
230C22×Dic5—64no—
231C22×Dic5—64no—
232C22×Dic5—64no—
233C22×Dic5D1214yescomplemented
234C22×Dic5C22×D311yescharacteristic
235C22×Dic5C22×D311yescharacteristic
236C22×Dic5C22×D311yescharacteristic
237C22×Dic5C22×D311yescharacteristic
238C5×C4⋊C4—34no—
239C5×C22⋊C4—38no—
240C22⋊Dic5—64no—
241C22⋊Dic5—64no—
242C22⋊Dic5—64no—
243C22⋊Dic5—64no—
244C4⋊Dic5—62no—
245C4⋊Dic5—62no—
246C4⋊Dic5—64no—
247C4×Dic5—22no—
248C4×Dic5—22no—
249C4×Dic5—22no—
250C4×Dic5—64no—
251C4×Dic5#6714yescomplemented
252C2×#121—31no—
253C2×C4×D4—151no—
254C2×C4×D4—152no—
255C22×C42—51no—
256#390—151no—
257#389—151no—
258#388—152no—
259#386—152no—
260#380—151no—
261C4×C4⋊C4—151no—
262C4×C22⋊C4—152no—
263C22×C3×C5—22no—
264C22×C3×C5—22no—
265C22×C3×C5—22no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5C4×D414yescomplemented
270C22×C3×C5C23×C411yescharacteristic
271C22×C3×C5C22×D411yescharacteristic
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C2×#4111yescharacteristic
274C22×C3×C5C2×#4111yescharacteristic
275C22×C3×C5C2×#4111yescharacteristic
276C22×C3×C5C2×#4111yescharacteristic
277C2×C5×D3—24no—
278C2×C5×D3—24no—
279C2×C5×D3—24no—
280C2×C5×D3—42no—
281C2×C5×D3—42no—
282C2×C5×D3—42no—
283C2×C5×D3—42no—
284C3×C4×C5—22no—
285C3×C4×C5C4×D414yescomplemented
286Dic15—42no—
287Dic15—42no—
288C3×Dic5—22no—
289C3×Dic5—22no—
290C3×Dic5—22no—
291C3×Dic5#12114yescomplemented
292C5×Dic3—24no—
293C24×C3C22×D511yescharacteristic
294C23×D3C22×D512yes—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—51no—
298C22×C3×C4—54no—
299C22×C3×C4—51no—
300C22×C3×C4—51no—
301C22×C3×C4—51no—
302C22×C3×C4—102no—
303C22×C3×C4—102no—
304C22×C3×C4—102no—
305C22×C3×C4—102no—
306C22×C3×C4—102no—
307C22×C3×C4C2×Dic514yescomplemented
308C22×C3×C4C22×D511yescharacteristic
309C22×C3×C4C22×D511yescharacteristic
310C2×#67—24no—
311C2×#67—24no—
312C2×#67C2×Dic518yescomplemented
313C22×Dic3—52no—
314C22×Dic3—52no—
315C22×Dic3C22×D512yes—
316C2×D12—22no—
317C2×D12—22no—
318C2×D12C2×Dic514yescomplemented
319C2×C4×D3—104no—
320C2×C4×D3—104no—
321C2×C4×D3—104no—
322C3×C42—54no—
323C3×C42—102no—
324C3×C42—102no—
325C3×C42—102no—
326#217—104no—
327(C2×D3)⋊C4—104no—
328(C2×D3)⋊C4—104no—
329(C2×D3)⋊C4—104no—
330(C2×D3)⋊C4C2×Dic518yescomplemented
331C4⋊Dic3—102no—
332C4⋊Dic3—102no—
333C4⋊Dic3C2×Dic514yescomplemented
334Dic3⋊C4—104no—
335C4×Dic3—104no—
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—21no—
340C23×C5—34no—
341C23×C5—62no—
342C23×C5—62no—
343C23×C5—62no—
344C23×C5—62no—
345C23×C5—62no—
346C23×C5—62no—
347C23×C5C2×C4×D312yes—
348C23×C5C2×D1212yes—
349C23×C5#23512yes—
350C23×C5C23×D311yescharacteristic
351C5×D4—616no—
352C5×D4—68no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—28no—
356C2×C4×C5—34no—
357C2×C4×C5—62no—
358C2×C4×C5—62no—
359C2×C4×C5C2×C4×D312yes—
360C2×C4×C5C2×C4×D312yes—
361C2×C4×C5#23512yes—
362C2×C4×C5C2×#6712yes—
363C2×Dic5—28no—
364C2×Dic5—21no—
365C2×Dic5—21no—
366C2×Dic5—21no—
367C2×Dic5—21no—
368C2×Dic5—21no—
369C2×Dic5—21no—
370C2×Dic5—28no—
371C2×Dic5—62no—
372C2×Dic5—62no—
373C2×Dic5—62no—
374C2×Dic5—62no—
375C2×Dic5—62no—
376C2×Dic5—62no—
377C2×Dic5—128no—
378C2×Dic5C2×D1212yes—
379C2×Dic5C2×D1212yes—
380C2×Dic5#23512yes—
381C2×Dic5#23512yes—
382C2×Dic5C2×#6712yes—
383C2×Dic5C2×#6712yes—
384C22×D4—32no—
385C22×D4—31no—
386C23×C4—51no—
387C23×C4—51no—
388C23×C4—152no—
389C23×C4D3×D511yescharacteristic
390#121—38no—
391C4×D4—304no—
392C4×D4—308no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—152no—
395C2×C4⋊C4—151no—
396C2×C4⋊C4—151no—
397C2×C22⋊C4—32no—
398C2×C22⋊C4—152no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C22⋊C4—152no—
402C2×C42—51no—
403C2×C42—51no—
404C2×C42—51no—
405C2×C42—51no—
406C2×C42—104no—
407C2×C42—152no—
408#95—152no—
409#95—152no—
410#95—152no—
411C2×C3×C5—24no—
412C2×C3×C5C2×C4×D411yescharacteristic
413C2×C3×C5C2×C4×D411yescharacteristic
414C2×C3×C5C4×#4111yescharacteristic
415C2×C3×C5C2×#12111yescharacteristic
416C2×C3×C5#52511yescharacteristic
417C2×C3×C5#52911yescharacteristic
418C2×C3×C5#53211yescharacteristic
419C5×D3—44no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3D4×D512yes—
425C23×C3#71112yes—
426C23×C3C22×Dic512yes—
427C23×C3C23×D511yescharacteristic
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3C22×Dic514yes—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—28no—
438C2×C3×C4—52no—
439C2×C3×C4—52no—
440C2×C3×C4—52no—
441C2×C3×C4—52no—
442C2×C3×C4—52no—
443C2×C3×C4—52no—
444C2×C3×C4—108no—
445C2×C3×C4—108no—
446C2×C3×C4—101no—
447C2×C3×C4—101no—
448C2×C3×C4—101no—
449C2×C3×C4—101no—
450C2×C3×C4—101no—
451C2×C3×C4—101no—
452C2×C3×C4D4×D512yes—
453C2×C3×C4#71112yes—
454C2×C3×C4C22×Dic512yes—
455C2×C3×C4C22×Dic512yes—
456#67—216no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—102no—
460C2×Dic3—102no—
461C2×Dic3—102no—
462C2×Dic3—102no—
463C2×Dic3—102no—
464C2×Dic3—102no—
465C2×Dic3C22×Dic514yes—
466D12—28no—
467C4×D3—208no—
468C22×C5—22no—
469C22×C5—22no—
470C22×C5—22no—
471C22×C5—22no—
472C22×C5—22no—
473C22×C5—22no—
474C22×C5—64no—
475C22×C5—64no—
476C22×C5—64no—
477C22×C5—122no—
478C22×C5—122no—
479C22×C5—122no—
480C22×C5—122no—
481C22×C5C4×D1214yescomplemented
482C22×C5C22×C4×D311yescharacteristic
483C22×C5C22×D1211yescharacteristic
484C22×C5C2×#23511yescharacteristic
485C22×C5C2×#23511yescharacteristic
486C22×C5C2×#23511yescharacteristic
487C22×C5C2×#23511yescharacteristic
488C22×C5C22×#6711yescharacteristic
489C4×C5—22no—
490C4×C5—64no—
491C4×C5C4×#6714yescomplemented
492Dic5—22no—
493Dic5—22no—
494Dic5—22no—
495Dic5—122no—
496Dic5—122no—
497Dic5#93014yesdirect product factor
498C24—32no—
499C24C2×D3×D511yescharacteristic
500C2×D4—38no—
501C2×D4—34no—
502C2×D4—64no—
503C2×D4—64no—
504C2×D4—62no—
505C2×D4—62no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—32no—
509C22×C4—51no—
510C22×C4—54no—
511C22×C4—51no—
512C22×C4—51no—
513C22×C4—51no—
514C22×C4—102no—
515C22×C4—102no—
516C22×C4—102no—
517C22×C4—102no—
518C22×C4—102no—
519C22×C4—152no—
520C22×C4—152no—
521C22×C4—304no—
522C22×C4—304no—
523C22×C4—304no—
524C22×C4D3×Dic514yescomplemented
525C22×C4C2×D3×D511yescharacteristic
526C22×C4C2×D3×D511yescharacteristic
527C4⋊C4—34no—
528C4⋊C4—304no—
529C4⋊C4—302no—
530C4⋊C4—302no—
531C22⋊C4—38no—
532C22⋊C4—304no—
533C22⋊C4—304no—
534C22⋊C4—304no—
535C22⋊C4—304no—
536C42—54no—
537C42—102no—
538C42—102no—
539C42—102no—
540C42—304no—
541C3×C5C4×#12111yescharacteristic, complemented, Hall
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3D4×Dic514yescomplemented
549C22×C3C2×D4×D511yescharacteristic
550C22×C3C2×D4×D511yescharacteristic
551C22×C3C2×#71111yescharacteristic
552C22×C3C2×#71111yescharacteristic
553C22×C3D5×#4111yescharacteristic
554C22×C3D5×#4111yescharacteristic
555C22×C3C23×Dic511yescharacteristic
556C2×D3—24no—
557C2×D3—24no—
558C2×D3—24no—
559C2×D3—42no—
560C2×D3—42no—
561C2×D3—42no—
562C2×D3—42no—
563C3×C4—22no—
564C3×C4—54no—
565C3×C4—102no—
566C3×C4—102no—
567C3×C4—102no—
568C3×C4D4×Dic514yescomplemented
569Dic3—24no—
570Dic3—202no—
571Dic3—202no—
572C2×C5—24no—
573C2×C5—124no—
574C2×C5C2×C4×D1211yescharacteristic
575C2×C5C4×#23511yescharacteristic
576C2×C5#547711yescharacteristic
577C2×C5#547911yescharacteristic
578C2×C5C2×C4×#6711yescharacteristic
579C2×C5C2×#93011yescharacteristic
580C2×C5#579111yescharacteristic
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—34no—
586C23—62no—
587C23—62no—
588C23—62no—
589C23—62no—
590C23—62no—
591C23—62no—
592C23#677212yes—
593C23D5×D1212yes—
594C23C2×D3×Dic512yes—
595C23C22×D3×D511yescharacteristic
596D4—616no—
597D4—68no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—28no—
601C2×C4—34no—
602C2×C4—52no—
603C2×C4—52no—
604C2×C4—52no—
605C2×C4—52no—
606C2×C4—52no—
607C2×C4—52no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—108no—
611C2×C4—108no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—101no—
618C2×C4—302no—
619C2×C4—302no—
620C2×C4—302no—
621C2×C4—302no—
622C2×C4—302no—
623C2×C4—302no—
624C2×C4—608no—
625C2×C4C2×D3×Dic512yes—
626C2×C4C2×D3×Dic512yes—
627C2×C4#678212yes—
628C2×C4D5×#6712yes—
629C2×C3—24no—
630C2×C3#6593011yescharacteristic
631C2×C3#6593411yescharacteristic
632C2×C3D5×#12111yescharacteristic
633C2×C3#6594011yescharacteristic
634C2×C3C2×D4×Dic511yescharacteristic
635C2×C3C2×D4×Dic511yescharacteristic
636C2×C3#41×Dic511yescharacteristic
637D3—44no—
638C5C4×#93011yescharacteristic, complemented, Sylow
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—64no—
646C22—64no—
647C22—64no—
648C22—122no—
649C22—122no—
650C22—122no—
651C22—122no—
652C22Dic5×D1214yescomplemented
653C22C2×#677211yescharacteristic
654C22C2×D5×D1211yescharacteristic
655C22D5×#23511yescharacteristic
656C22D5×#23511yescharacteristic
657C22C22×D3×Dic511yescharacteristic
658C22C2×#678211yescharacteristic
659C22C2×D5×#6711yescharacteristic
660C4—22no—
661C4—54no—
662C4—64no—
663C4—102no—
664C4—102no—
665C4—102no—
666C4—602no—
667C4—602no—
668C4Dic5×#6714yescomplemented
669C3Dic5×#12111yescharacteristic, complemented, Sylow
670C2—24no—
671C2—124no—
672C2C2×Dic5×D1211yescharacteristic
673C2#1175433011yescharacteristic
674C2Dic5×#23511yescharacteristic
675C2#1175441011yescharacteristic
676C2#1175452611yescharacteristic
677C2D5×#93011yescharacteristic
678C2C2×Dic5×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#930C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C3×C4×Dic5C2semidirect
3. C2×Dic5×#67C2semidirect
4. C2×Dic5×D12C2semidirect
5. #11751313C2semidirect
6. #11749492C2semidirect
7. Dic5×(C2×D3)⋊C4C2semidirect
8. #11748842C2semidirect
9. #11748764C2semidirect
10. #11748747C2semidirect
11. Dic5×C4⋊Dic3C2semidirect
22. C5×#930C4semidirect
44. C22×C4×Dic5D3semidirect
56. C22×C3×C4×C5C2×C4semidirect
63. C2×C5×#67C2×C4semidirect
67. C2×C5×D12C2×C4semidirect
73. C22×C3×Dic5D4semidirect
84. C5×(C2×D3)⋊C4C2×C4semidirect
85. C5×C4⋊Dic3C2×C4semidirect
89. C3×C4×Dic5D4semidirect
194. #930Dic5direct (N × H)
220. C22×C4×C5C4×D3semidirect
233. C22×Dic5D12semidirect
251. C4×Dic5#67semidirect
269. C22×C3×C5C4×D4semidirect
285. C3×C4×C5C4×D4semidirect
291. C3×Dic5#121semidirect
307. C22×C3×C4C2×Dic5semidirect
312. C2×#67C2×Dic5semidirect
318. C2×D12C2×Dic5semidirect
330. (C2×D3)⋊C4C2×Dic5semidirect
333. C4⋊Dic3C2×Dic5semidirect
481. C22×C5C4×D12semidirect
491. C4×C5C4×#67semidirect
497. Dic5#930direct (N × H)
524. C22×C4D3×Dic5semidirect
541. C3×C5C4×#121semidirect
548. C22×C3D4×Dic5semidirect
568. C3×C4D4×Dic5semidirect
638. C5C4×#930semidirect
652. C22Dic5×D12semidirect
668. C4Dic5×#67semidirect
669. C3Dic5×#121semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C5×#9302
C22×C3×C4×Dic52
C2×Dic5×#672
C2×Dic5×D122
#117513132
#117494922
Dic5×(C2×D3)⋊C42
#117488422
#117487642
#117487472
Dic5×C4⋊Dic32
Dic5×#1213
C4×#9305